Topological Invariant and Quantum Spin Models from MagneticπFluxes in Correlated Topological Insulators

@article{Assaad2013TopologicalIA,
  title={Topological Invariant and Quantum Spin Models from Magnetic$\pi$Fluxes in Correlated Topological Insulators},
  author={Fakher F. Assaad and Martin Bercx and Martin Hohenadler},
  journal={Physical Review X},
  year={2013},
  volume={3}
}
The adiabatic insertion of a \pi flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that \pi fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_2 topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a \pi flux gives rise to a Kramers doublet of spinon states with a Curie law signature in the magnetic susceptibility. Electronic correlations… 
9 Citations

Kane-Mele-Hubbard model on theπ-flux honeycomb lattice

We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the

Quantum cluster approach to the spinful Haldane-Hubbard model

We study the spinful fermionic Haldane-Hubbard model at half-filling using a combination of quantum cluster methods: cluster perturbation theory, the variational cluster approximation, and cluster

Thermodynamic and topological phase diagrams of correlated topological insulators

A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. The

Breakdown of topological Thouless pumping in the strongly interacting regime

We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of

Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH)

Nichtperturbative Linked-Cluster Entwicklungen für unkonventionelle Mottisolatoren

In this thesis linked-cluster expansions are further developed and applied to different Hubbard and spin models at zero temperature. The spin models can be viewed as effective descriptions of the

Correlation effects in two-dimensional topological insulators

TLDR
This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results.

Comparing the effective enhancement of local and nonlocal spin-orbit couplings on honeycomb lattices due to strong electronic correlations

Markus Richter, Johannes Graspeuntner, Thomas Schäfer, Nils Wentzell, and Markus Aichhorn ∗ Institute of Theoretical and Computational Physics, Graz University of Technology, NAWI Graz, Petersgaße

The ALF (Algorithms for Lattice Fermions) project release 2.0. Documentation for the auxiliary-field quantum Monte Carlo code

TLDR
The Algorithms for Lattice Fermions package provides a general code for the finite temperature auxiliary field quantum Monte Carlo algorithm and discusses how to use the package to implement the Kondo lattice model and the $SU(N)$-Hubbard-Heisenberg model.

References

SHOWING 1-10 OF 62 REFERENCES

Topological insulators and Mott physics from the Hubbard interaction

We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions.

Topological insulators and quantum spin liquids

Quantum spin-Hall effect and topologically invariant Chern numbers.

TLDR
It is shown that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers, and the nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM).

Topological order and semions in a strongly correlated quantum spin Hall insulator.

TLDR
This work identifies an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction that is gapped and does not break any symmetry, and argues that it has gapless edge modes protected by time-reversal symmetry but a trivial Z(2) topological invariant.

One-dimensional topologically protected modes in topological insulators with lattice dislocations

Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems such as the B-phase of superfluid helium He3, where vortices are

Topological semimetal in a fermionic optical lattice

Experimental progress has made it possible to load fermionic atoms into higher orbital bands. Such systems provide a platform for studying quantum states of matter that have no prior analogues in

Quantum spin liquid emerging in two-dimensional correlated Dirac fermions

TLDR
It is shown, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermion and an antiferromagnetically ordered Mott insulator.

Quantum spin Hall insulators with interactions and lattice anisotropy

We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice, combining the cellular dynamical mean-field theory and its real-space extension

Universal probes of two-dimensional topological insulators: dislocation and π flux.

TLDR
It is conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.

Correlation effects on a topological insulator at finite temperatures

We analyze the effects of the local Coulomb interaction on a topological band insulator (TBI) by applying the dynamical mean-field theory to a generalized Bernevig-Hughes-Zhang model having electron
...